Unitarity bounds on extensions of Higgs sector

TL;DR

This paper derives unitarity bounds on extended Higgs models, specifically those adding triplet scalars to the two-Higgs-doublet model, providing analytic constraints and numerical bounds on model parameters.

Contribution

It develops a method to classify two-body scalar scatterings using gauge symmetry decomposition and applies it to derive unitarity bounds on extended Higgs models with triplet scalars.

Findings

Unitarity bounds constrain model parameters effectively.

Analytic expressions for scattering matrix eigenvalues are derived.

Numerical analysis shows bounds are stringent for complex triplet extensions.

Abstract

It is widely believed that extensions of the minimal Higgs sector is one of the promising directions for resolving many puzzles beyond the Standard Model (SM). In this work, we study the unitarity bounds on the models by extending the two-Higgs-doublet model with an additional real or complex Higgs triplet scalar. By noting that the SM gauge symmetries $SU(2)_L\times U(1)_Y$ are recovered at high energies, we can classify the two-body scattering states by decomposing the direct product of two scalar multiplets into their direct sum of irreducible representations of electroweak gauge groups. In such state bases, the s-wave amplitudes of two-body scalar scatterings can be written in the form of block-diagonalized scattering matrices. Then the application of the perturbative unitarity conditions on the eigenvalues of scattering matrices leads to the analytic constraints on the model parameters. Finally, we numerically investigate the complex triplet scalar extension of the two-Higgs-doublet model, finding that the perturbative unitarity places useful stringent bounds on the model parameter space.